No! Not a firing squad nor the need for a continuous line to cross all line segments just once!

To each vertex labeled A to L apply a different value from 1 to 12. Let V, W, X, Y and Z be the sums of their respective surrounding vertices.

Provide at least one example where V=W=X=Y=Z, or offer a reason why this, like the continuous line, is impossible.

If one considers "vertex" as limiting the sums of each rectangle to the corners (i.e. leaving out F, G, and H from the sums of Y, W, and Z respectively) there will be a set of sums for each method.  If, for each method of calculating, one lists the numbers which occur as sums, there is an interesting difference in these lists.  For one the possibilities are all consecutive; for the other there is a gap in the possible sums.  Can you identify?

 

Posted by ed bottemiller on 2010-04-29 16:40:14